Whether you wanted it or not, here's my story. I don't like Renault garages (I have reason not to trust them) but last year I left my mot really late, and Renault Manchester is only 5 mins. from work - I thought it's just an mot, what could go wrong? So booked my car in. Being the idiot I am, I only checked the lights at about 9:30 the night before and found my number plate light wasn't working - couldn't buy a new bulb before I took it in. Arrived early and told them my light wasn't working - could they put a new bulb in for me before the mot. Sure no problem they said, that'll be £16. WHAT, THAT'S RIDICULOUS I said, I've even unclipped the light for you. Ok we can do it for £11. Right can I buy a bulb from you and do it myself - sure, the parts department will be open in 20 mins. NNRRRGGHHH. Had no choice but to leave it with them, needed to get to work. Got a call later - car had failed. Apparently wasn't just the bulb, needed new light fitting and section of wiring - would I like them to fit it for me at a cost of around £79. NO, I'll do it myself. So collected the car, and bought myself a new bulb (least I avoided their extortionate bulb fitting charge.) Unclipped the light, disconnected the plug, and there was some corrosion on the contacts. Got a screwdriver and scraped it off, reconnected, new bulb in - and IT WORKED! A whole 5 mins of work. I wished I'd just tried a new bulb straight off - maybe it would have worked anyway. Then had the hassle of booking my car back in for a re-test. Nearly a year later, and still working fine. To be on the safe side, weekend before last, I removed the light again and did a propper job of it. Dissassembled it as much as I could, scraped off the corrosion I could reach, gave it all a good clean, applied grease to the contacts, and put it all back together. Hopefully it will last a while.
Sorry, just needed to vent
I don't know exactly what's wrong with yours - maybe the contacts have corroded away, maybe the wiring is knackered. But if you're just trusting the word of a garage, you may as well have a look yourself, complicated it ain't - a wire leading to a bulb basically. It can't do any harm to have a go, and you could save yourself some cash. If you do have a look yourself, just be careful to protect the paintwork of the bumper when removing the light. If you're using a screwdriver wrap masking tape or a piece of paper around the end of it. As you probably know - don't touch the glass of car bulbs with your fingers, use a tissue or something (if you do accidentally, use methylated spirits to clean the glass.)
Sorry for the rant, best of look.
(Longest response on record?)